1. Field of the Invention
This invention relates to an estimation method, and more specifically to a method for estimating the frequency shift of a CPFSK signal.
2. Description of the Related Art
Digital receiver systems for frequency or phase modulated signals, in particular for CPFSK signals (“Continuous Phase Frequency Shift Keying”) frequently also requite, for correct and highly efficient detection of the transmitted symbols, apart from symbol synchronisation, digital estimation and correction of a possible phase or frequency shift.
For the purpose of estimating the frequency shift intuitive methods are used which employ known signal characteristics or characteristics from signals derived from the incoming signal, as well as methods which are based on the so-called ML principle (“Maximum Likelihood”). In this case basically a distinction is made between data-aided and non-data-aided as well as clock-aided and non-clock-aided methods. In addition a distinction can be made between estimating methods without feed back (feed forward or open loop) and estimating methods with feed back (closed loop).
In “Synchronisation Techniques for Digital Receivers” U. Mengali and A. N. D'Andrea, Plenum Press, New York, 1997 a number of known methods for estimating the digital frequency shift are described whereby in particular a non-data-aided, though clock-aided estimating method for MSK signals (“Minimum Shift Keying”) is presented, which relies on the so-called “Delay and Multiply” principle. A differential demodulator is used as an essential component in this case. This known method will be explained below in more detail.
With this known method it is firstly assumed that an MSK incoming signal r(t) is filtered for noise limitation and the resultant filtered MSK incoming signal x(t) is scanned at predetermined intervals kT+τ, whereby k designates the scanning index, T the symbol duration of the incoming signal and τ a delay constant. As described in more detail in “Synchronisation Techniques for Digital Receivers”, U. Mengali and A. N. D'Andrea, Plenum Press, New York, 1997, an intermediate signal z(k·T+τ) can be derived from the filtered and scanned complex envelope x(k·T+τ) of the incoming signal (as well as the corresponding conjugated complex signal x*(k·T+τ)) as follows:z(k·T+τ)=x2(k·T+τ)·{x2([k−1]·T+τ)}*={x(k·T+τ)·x*([k−1]·T+τ)}2
This intermediate signal gives the estimated value for the frequency shift ν by assessing an observation interval including L0 receiver symbols:
  v  =                              -                      1                          4              ⁢              π              ⁢                                                          ⁢              T                                      ·        arg            ⁢              {                              z            ⁡                          (              τ              )                                +                      z            ⁡                          (                              T                +                τ                            )                                +                      z            ⁡                          (                                                2                  ·                  T                                +                τ                            )                                +                                          ⁢                      .                                                  .                                                  .                                                  ⁢                          +                              z                ⁡                                  (                                                                                    [                                                                              L                            0                                                    -                          1                                                ]                                            ·                      T                                        +                    τ                                    )                                                                    }              =                            -                      1                          4              ⁢              π              ⁢                                                          ⁢              T                                      ·        arg            ⁢              {                              ∑                          k              =              0                                                      L                0                            -              1                                ⁢                                          ⁢                      z            ⁡                          (                                                k                  ·                  T                                +                τ                            )                                      }            
As already mentioned, the method described above however concerns a model developed for MSK incoming signals. During MSK modulation the carrier phase during the time T of a symbol is rotated around the amount
      ±          π      2        ,so that the frequency of the transmitted signal, dependent on the symbol being transmitted, changes between
      ϖ    0    +      π          2      ·      T      and
            ϖ      0        -          π              2        ·        T              ,whereby ω0 designates the nominal carrier frequency.
In the case of angle-modulated signals the phase of the carrier signal is changed in harmony with a phase function q(t) of a suitable phase filter. For MSK signals the phase function is defined as follows:
      q    ⁡          (      t      )        =      {                            0                                      t            <            0                                                            t            T                                                0            ≤            t            <            T                                                1                                      t            >            T                              
The phase function q(t) therefore assumes its end value after the duration T of a transmitted symbol.
CPFSK signals however generally possess a phase function, in contrast to MSK signals, which only reach their end value after an interval of time L·T where L>1, that is to say the phase function q(t) for CPFSK signals is defined as follows:
      q    ⁡          (      t      )        =      {                            0                                      t            <            0                                                            q            ⁡                          (              t              )                                                            0            ≤            t            <                          L              ·              T                                                            1                                      t            >                          L              ·              T                                          